Email this article Binomial sequences
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References
Aceto, Lidia and Isabel Cação. "A matrix approach to Sheffer polynomials." J. Math. Anal. Appl. 446, no. 1 (2017): 87-100.
Berthelot, Pierre Cohomologie cristalline des schémas de caractéristique p > 0. Vol. 407 of Lecture Notes in Mathematics. Berlin-New York: Springer-Verlag, 1974.
Brand, Louis. "Binomial expansions in factorial powers." Amer. Math. Monthly 67 (1960): 953-957.
Brown, J.W. "On zero type sets of Laguerre polynomials." Duke Math. J. 35 (1968): 821-823.
Di Bucchianico, A. Probabilistic and analytical aspects of the umbral calculus. Vol. 119 CWI Tract. Amsterdam: Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, 1997
Carlitz, L. "Some generating functions for Laguerre polynomials." Duke Math. J. 35 (1968), 825-827.
Comtet, Louis. Advanced combinatorics. The art of finite and infinite expansions. Dordrecht: D. Reidel Publishing Co., 1974.
Ekhad, Shalosh B. and John E. Majewicz. "A short WZ-style proof of Abel’s identity." Electron. J. Combin. 3, no. 2 (1996): Research Paper 16, approx. 1 p.
Foata, Dominique. "Enumerating k-trees." Discrete Math. 1, no. 2 (1971/72): 181-186.
Graham, Ronald L., Donald E. Knuth and Oren Patashnik. Concrete mathematics. A foundation for computer science. Reading, MA: Addison-Wesley Publishing
Company, 1989.
Huang, Fengying and Bolian Liu. "The Abel-type polynomial identities." Electron. J. Combin. 17, no. 1, (2010): Research Paper 10, 7 pp.
Kisil, Vladimir V. "Polynomial sequences of binomial type and path integrals." Ann. Comb. 6, no. 1, (2002): 45-56.
Krall, H.L. "Polynomials with the binomial property." Amer. Math. Monthly 64 (1957): 342-343.
Lipnowski, M. "A solution of Problem 310." Vol. 5 of Olymon – Mathematical Olympiads’ Correspondence Program. Canada: Canadian Mathematical Society, 2004.
Mihoubi, Miloud. "Bell polynomials and binomial type sequences." Discrete Math. 308, no. 12 (2008): 2450-2459.
Młotkowski, Wojciech and Romanowicz, Anna. "A family of sequences of binomial type." Probab. Math. Statist. 33, no. 2 (2013): 401-408.
Nowicki, Andrzej. Arithmetic functions Vol.5 of Podróze po Imperium Liczb. Torun, Olsztyn: Wydawnictwo OWSIiZ, 2012.
Nowicki, Andrzej. Factorials and binomial coefficiens, Vol. 11 of Podróze po Imperium Liczb. Torun, Olsztyn: Wydawnictwo OWSIiZ, 2013.
Petrullo, Pasquale. "Outcomes of the Abel identity." Mediterr. J. Math. 10, no. 3 (2013): 1141-1150.
Roman, Steven M. and Gian-Carlo Rota. "The umbral calculus." Advances in Math. 27, no. 2 (1978): 95-188.
Rota, Gian-Carlo, D. Kahaner and A. Odlyzko, "On the foundations of combinatorial theory. VIII. Finite operator calculus." J. Math. Anal. Appl. 42 (1973): 84-760.
Rota, Gian-Carlo, Jianhong Shen and Brian D. Taylor. "All polynomials of binomial type are represented by Abel polynomials." Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25, no. 3-4 (1997): 731-738.
Schneider, Jonathan. "Polynomial sequences of binomial-type arising in graph theory." Electron. J. Combin. 21, no. 1 (2014): Paper 1.43, 17 pp.
Sheffer, I.M. "Some properties of polynomial sets of type zero." Duke Math. J. 5 (1939): 590-622.
Shukla, A.K. and S.J. Rapeli. "An extension of Sheffer polynomials." Proyecciones 30, no. 2 (2011): 265-275.
Sykora, S. "An Abel’s identity and its corollaries." Preprint, 2014. Cited on 115.
Zheng, G. "A solution of Problem 310." Vol. 5 of Olymon – Mathematical Olympiads’ Correspondence Program. Canada: Canadian Mathematical Society, 2004.
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